A defense system against an air-to-surface missile (ASM) incorporates many types of sensors, such as image sensor, lidar, and radar, for detecting the location, velocity and acceleration of the target ASM.
The image sensors have low capability of sensing depth and high capacity of target discrimination than lidar and radar. The radar shows limited lateral spatial information, and has a narrow field of view and a reduced resolution at large distance. Although the lidar has a wide field of view, the lidar has low capacity of target discrimination and also suffers from high clustering error.
Precise detection of a high-speed target missile is the key to an effective missile defense system. Several methods have been disclosed to trilaterate a specific target based on multiple radar detections. For example, a target can be trilaterated based on the echo wave signal of the multiple frequency-modulated continuous wave (FMCW).
Kalman filters are commonly used to track maneuvering target. A one-stage linear Kalman filter estimates the relative range and relative velocity based on the measurement data of relative range. However, the acceleration cannot be accurately estimated when the target is making a turn in a short period.
A two-stage linear Kalman filter is similar to the one-stage linear Kalman filter, except with a new bias vector to estimate the relative acceleration. However, the convergence time is too long to be of practical use.
An extended Kalman filter can be used to estimate all the kinetic parameters of the target using only one sensor. However, the error of some parameters can be too large when the target is making a turn. Many methods for missile detection are disclosed in prior arts. For example, one prior reference disclosed a method using an antenna array to apply the maximum likelihood estimation (MLE) to obtain the normalized spatial and Doppler frequency of the echo signal of the target, and map to the direction and relative velocity of the target. However, this method requires 64 samples, which requires more time. As an antenna array is used, the observed values from plural sensors must be computed simultaneously; thus, the computation is more complicated.
Another prior reference disclosed a method using the extended Kalman filter and recursive prediction error method to compute the relative acceleration with error only half that of using extended Kalman filter alone. However, the variance of the result from this method is large, and thus, the result is not sufficiently stable.
Yet another prior reference disclosed a method using a two-stage Kalman filter to obtain the directional components of the location. However, this method is only applicable to predicting the location when the relative acceleration is known, and is not applicable to predicting the precise location of the next time.
Yet another prior reference disclosed a method using matched filter to apply planar transformation of distance and velocity to find the most concentrated point, called initial distance r0 and velocity v0, under the condition of scanning the known relative velocity range. Although the relative velocity range of the target is known, the number of samples can be controlled within 30 with improved precision. However, there is still room for further improvement as 30 samples and planar transformations are still considered complicated.
Another prior reference disclosed a method using linear frequency modulation (LFM) with fast MLE to obtain the target location. This method requires Hough transformation for rough estimation and Newton method for obtaining more accurate solution. This method is unable to obtain the acceleration, and requires more time to measure and compute.
Yet another prior reference disclosed a method combining frequency shift key (FSK) and LFM. This method requires a sensor to alternately receiving and transmitting two sets of signals with different frequencies. Although this method is fast, the method cannot obtain the relative acceleration of the target.
Yet another prior reference disclosed a method using plural, for example 128, received samples to obtain the correlation and then compute the relative velocity and relative acceleration. As more received samples are used, this method requires more time.
Another prior reference disclosed a method multiplying the current received signal with the signal of the previous time, and through the transformations to compute the relative velocity and the relative acceleration. This method also requires N received samples.
Yet another prior reference disclosed a method by substituting two-stage Kalman filter with robust two-stage Kalman filter so that the application is simplified. However, this architecture is a linear system, and it remains a problem for applicability to non-linear system.
Yet another prior reference disclosed a method using trajectory tracking technology. Through the observed distance r and velocity v, Kalman filter is used to computer x, y, x, vx, vy and vz. The first approach uses plural sensors to compute the intersection of the distance and the variance of the intersection. Then, the linear Kalman filter is used for tracking. The advantages of this approach are the clear workload distribution and the high precision of the computation. However, the amount of computation is high and the ghost targets may occur. The second approach is to use the pre-computed distance r and velocity v to track through the extended Kalman filter in a nonlinear manner. Because each sensor can compute a target, the ghost targets are less likely to occur. The third approach is to use only the distance r to track through the extended Kalman filter in a nonlinear manner. This approach is simple and fast, but the precision of vx and vy will be reduced.
Yet another prior reference disclosed a method using standard Kalman filter to estimate a fixed relative acceleration after the relative location and the velocity estimation. However, this method takes more time to converge.
Yet another prior reference disclosed a method directly using the two-stage extended Kalman filter to obtain x, y, z, vx, vy, vz, ax, ay, and az from the observed distance r and velocity v. However, this method does not perform well in the precision of ax, ay, and az.
Yet another prior reference disclosed a method using the three previous observations to predict the relative acceleration ax, ay, and az. Then, a weighting factor is used to re-modify the x, y, z, vx, vy, and vz. This method has high accuracy in linear acceleration, but has a low accuracy in acceleration when the target missile makes turns.
Another prior reference disclosed a method first computing x, y, z, and then using the linear Kalman filter to estimate x, y, z, vx, vy, and vz. Under the condition that the relative acceleration is known, this method is applicable only to location detection, not to location prediction of the next time.
U.S. Pat. No. 5,051,751 disclosed a method of using the Kalman to estimate the location and velocity of a flying target. By using the Kalman filter to establish a measurement architecture and using a sensor architecture to obtain a sensor measurement, the sensor measurement is transformed to the measurement architecture, and the value is used to update the Kalman filter. The position/velocity error states are used to calibrate the trajectory model for the prediction at the next time.
U.S. Pat. No. 5,208,757 disclosed a system of determining the flying target location. The first memory includes different types of landmarks, and the second memory includes the location of the landmarks. By using a sensor to receive the signal from the landmarks, the system then uses the Kalman filter to compute the relative location of the flying target.
U.S. Pat. No. 5,525,995 disclosed a radar system of detecting the location and trajectory of the target using Doppler effect. By using a nonlinear least square (NLS) estimator to detect the initial velocity and initial location of the target, the system then uses the Kalman filter to predict the trajectory. The difference between the measurement and the Doppler-effect estimation is then used as in index to the predicted trajectory.
U.S. Pat. No. 6,082,666 disclosed a system of accurate prediction of vertical velocity and height of missiles. The system can be installed on a missile to combine with Kalman filter application. The Kalman filter consists of two parts. The first part is the vertical velocity of the missile, and the second part is the vertical height of the missile.
U.S. Pat. No. 6,845,938 disclosed an apparatus of periodically guiding targets. The apparatus constructs a re-constructed line-of-sight (LOS) and uses harmonically balanced Kalman filter banks to construct a set of guidance command signals. The signal set is perpendicular to the LOS of the target, and the signal is used to an automatic navigator.
U.S. Pat. No. 7,034,742 disclosed an application of two Kalman filters. The first Kalman filter can predict the vehicle state from the yaw rate and speed of the moving vehicle, and the second Kalman filter obtains the road curvature parameters. The system is applicable to warning system, safety system and vehicle control system.
U.S. Pat. No. 7,046,188 disclosed a system and method of tracking target. In the embodiment of the disclosed patent, when a target is detected, the Kalman filter is used for tracking. After losing the detection, a blind zone particle filter can be used until the probability that the target is located in the blind zone exceeds a threshold. When the probability that the target is in the unrestricted zone is higher than the threshold, the blind zone particle filter and the unrestricted zone particle filter can compute simultaneously. Then, the system can resume the Kalman filter for tracking.